This invention relates to structures for generating controllable magnetic fields. Among other things, the invention has application to control systems for nonlinear optical devices. More particularly, this invention relates to an axially symmetric permanent magnet structure capable of generating tunable magnetic fields directed along the axis of the magnet structure. The invention can be used to precisely tune the strength of longitudinal fields within the central region of the axially symmetric structure.
Strong alternating polarity axial magnetic fields using an array of low volume permanent magnets were first used in the 1980's by Klaus Halbach to focus accelerator particle beams. The arrays had the additional feature of very low external fields along the outer surfaces of the array. Truncated forms of these “Halbach arrays” can generate high unidirectional longitudinal fields in excess 10,000 Oersted within the center of axially symmetric magnet structures using low-cost neodymium iron boron permanent magnets. Such magnet structures have been widely used in Faraday rotators.
Faraday rotators are used to achieve non-reciprocal polarization rotation in optical systems. They are also widely used in “Faraday-effect” devices such as optical isolators, optical circulators, and Faraday mirrors in either polarization maintaining [PM] or polarization independent or polarization insensitive [PI] forms, as appropriate, in many laser systems. Optical isolators are used to block external reflections and/or noise emission from amplifiers that may cause instability or damage if permitted to re-enter a laser source. Proper operation of these Faraday-effect devices typically requires precisely 45° of non-reciprocal polarization (“Faraday”) rotation at a specific wavelength and/or temperature. The amount of Faraday rotation is given by:θ(λ,T)=V(λ,T)×H(T)×L  (1).where:                θ(λ,T): The Faraday rotation angle (a function of wavelength, λ; temperature, T);        V(λ,T): A proportionality constant, termed the Verdet constant, of the optical element (a function of wavelength, λ, and temperature, T);        H(T): The strength of the magnetic field in the direction of light through the optical element (a function of temperature, T); and        L: The length of the optical element.        
The high values for H(T) achieved with truncated Halbach arrays minimize the length L of the Faraday rotator optical element required. This is preferable because undesirable thermal lensing and thermal birefringence at high average optical power due to absorption in the Faraday optical element increases with increasing length L.
The Verdet constant V(λ,T) is a function of both wavelength and temperature, and the magnetic field H(T) is a function of temperature. It follows for a fixed optical element length L that the product H(T)×L will typically need to be adjusted in order to achieve the desired 45° Faraday rotation angle θ(λ,T) at an arbitrary temperature and/or wavelength.
When the magnetic field H(T) varies in strength along the axis of light propagation (as in a truncated Halbach array), it is possible in some contexts to physically translate the Faraday optic element relative to the magnet structure in order to vary the product H(T)×L and thereby precisely adjust the rotation angle θ(λ,T). However, optical isolators and circulators can be extremely sensitive to any change in orientation or position of optical elements—particularly when both the input and output are fiber coupled. For such devices mechanical stability of the structure may require that the optics remain fixed in position. Hence, in cases where it is impractical or undesirable to translate the Faraday optic element, what is needed is a means of tuning the strength of axial magnetic fields in the vicinity of a fixed Faraday optic to achieve precisely 45° of Faraday rotation.
Referring to FIG. 1, a truncated Halbach array of the prior art that is used to generate high magnetic fields for Faraday rotation is shown in a cross-sectional diagram. A hollow housing tube 2 and dual endplate screws 3 threaded into each end of the tube 2 together enclose permanent magnet radial sectors 4 and 5 and a center axial magnet 6 of toroidal construction, which are all centered around axis 1 and a Faraday optic element 7. The magnetization arrows shown indicate that all radial sectors 4 have a North pole at their inner surfaces, whereas all radial sectors 5 have a South pole at their inner surfaces. Center axial magnet 6 is disposed to exhibit magnetization along axis 1 such that it opposes the inner surfaces (like poles) and attracts the outer surfaces (opposite poles) of radial sectors 4 and 5. In a typical Faraday Rotator, there are four or more radial sectors 4 and 5 on either side of center axial magnet 6. Ideally in a conventional Halbach array, radial sector magnets 4 and 5 could be a single immovable ring with magnetization everywhere directed radially with respect to axis 1. Such single ring radial magnets would have the highest efficiency. However, such magnets are not readily attainable using high strength permanent magnets and would also require an expensive magnetizing fixture requiring extremely high discharge currents to generate radial magnetizing fields. For these practical reasons, an ideal single ring radial magnet is approximated with a ring comprised of two or more radial sectors—with more sectors held rigidly in place and forming a better approximation of an ideal radial magnet ring. The outer and/or inner surface of these axially symmetric magnetic structures can be circular as shown, or square or rectangular as appropriate. Housing tube 2 may be of ferrous or non-ferrous material. Endplate screws 3 will typically be a non-ferrous material so as to not provide a leakage path for magnetic flux generated by the radial sectors 4 and 5.
Arranged and magnetized in this fashion, the radial sectors 4 and 5 and the center axial magnet 6 together form a truncated Halbach array which can generate high magnetic fields directed along axis 1 in the region of Faraday optic 7, enabling instantiation of a Faraday rotator of compact dimensions. Such Faraday rotators have found widespread use with high power lasers in the wavelength range of 1030 nm to 1080 nm when a rod of approximately 2 cm in length of terbium gallium garnet “TGG” is used as the Faraday optic 7.
FIG. 2 shows a plot of the magnetic field strength along axis 1 of FIG. 1 when four radial sectors 4 and 5 form separate rings of dimension 34.5 mm OD×6.1 mm ID×13.0 mm thick and Center Axial magnet 6 has dimensions 34.5 mm OD×6.1 mm ID×12.0 mm thick. At 20° C. the residual induction of radial sectors 4 and 5 used is 13.0 kG and the intrinsic coercivity is 17 kOe. The residual induction of center axial magnet 6 as used is 11.2 kG and the intrinsic coercivity is 30 kOe at 20° C. With a 2 cm TGG Faraday optic 7 centered in the magnet structure, the average magnetic field H along axis 1 over the length of the TGG Faraday optic at 23° C. is Havg(23° C.)=11.55 kOe.
Nd—Fe—B magnets, such as those used in the above models, have a reversible temperature coefficient of −0.11%/° C. Hence the average magnetic field along axis 1 over the length of the 2 cm TGG is 11.84 kOe, 11.59 kOe, 11.34 kOe, and 11.08 kOe at 0°, 20°, 40° and 60° C., respectively.
In practice, variations in the strength of individual permanent magnets comprising a magnetic structure and/or variations in the Faraday rotation element can also change the expected Faraday rotation angle θ(λ,T) by as much as 5 to 10%. This is a further practical impetus for seeking means to tune the magnetic field H(T).